Is it possible to sharpen a hedgetrimmer? If so, how?

The most important thing about sharpening these or scissors is not to grind from both sides. You want a sharp edge facing onto a flat face so that when it is reembled the two sharp edges are really close together. If you grind the smallest bevel on the facing side then there will be double that gap between the two cutting edges when reembled and it will cut badly. All you should do on the facing side is remove the burr you raise up by grinding the angled edge. I would use a new file. It is very easy to overheat the edge with a power tool then it may feel sharp but the temper is lost and it will be blunt again in no time.